Systems, methods, and apparatus for automatic image recognition

ABSTRACT

A method of improving the accuracy and computation time of automatic image recognition by the implementation of association graphs and a quantum processor.

CROSS REFERENCE TO RELATED APPLICATIONS

This application claims benefit under 37 C.F.R. 119(e) of U.S.Provisional Patent Application Ser. No. 60/912,904, filed Apr. 19, 2007,entitled “Systems, Methods, and Apparatus for Automatic ImageRecognition”, which is incorporated herein by reference in its entirety.

BACKGROUND

1. Field

The present systems, methods, and apparatus relate to the implementationof a quantum processor in the automatic recognition of an image, such asa facial image, from a database of images.

2. Description of the Related Art

A Turing machine is a theoretical computing system, described in 1936 byAlan Turing. A Turing machine that can efficiently simulate any otherTuring machine is called a Universal Turing Machine (UTM). TheChurch-Turing thesis states that any practical computing model haseither the equivalent or a subset of the capabilities of a UTM.

A quantum computer is any physical system that harnesses one or morequantum effects to perform a computation. A quantum computer that canefficiently simulate any other quantum computer is called a UniversalQuantum Computer (UQC).

In 1981 Richard P. Feynman proposed that quantum computers could be usedto solve certain computational problems more efficiently than a UTM andtherefore invalidate the Church-Turing thesis. See e.g., Feynman R. P.,“Simulating Physics with Computers”, International Journal ofTheoretical Physics, Vol. 21 (1982) pp. 467-488. For example, Feynmannoted that a quantum computer could be used to simulate certain otherquantum systems, allowing exponentially faster calculation of certainproperties of the simulated quantum system than is possible using a UTM.

Approaches to Quantum Computation

There are several general approaches to the design and operation ofquantum computers. One such approach is the “circuit model” of quantumcomputation. In this approach, qubits are acted upon by sequences oflogical gates that are the compiled representation of an algorithm.Circuit model quantum computers have several serious barriers topractical implementation. In the circuit model, it is required thatqubits remain coherent over time periods much longer than thesingle-gate time. This requirement arises because circuit model quantumcomputers require operations that are collectively called quantum errorcorrection in order to operate. Quantum error correction cannot beperformed without the circuit model quantum computer's qubits beingcapable of maintaining quantum coherence over time periods on the orderof 1,000 times the single-gate time. Much research has been focused ondeveloping qubits with coherence sufficient to form the basicinformation units of circuit model quantum computers. See e.g., Shor, P.W. “Introduction to Quantum Algorithms”, arXiv.org:quant-ph/0005003(2001), pp. 1-27. The art is still hampered by an inability to increasethe coherence of qubits to acceptable levels for designing and operatingpractical circuit model quantum computers.

Another approach to quantum computation involves using the naturalphysical evolution of a system of coupled quantum systems as acomputational system. This approach does not make critical use ofquantum gates and circuits. Instead, starting from a known initialHamiltonian, it relies upon the guided physical evolution of a system ofcoupled quantum systems wherein the problem to be solved has beenencoded in the terms of the system's Hamiltonian, so that the finalstate of the system of coupled quantum systems contains informationrelating to the answer to the problem to be solved. This approach doesnot require long qubit coherence times. Examples of this type ofapproach include adiabatic quantum computation, cluster-state quantumcomputation, one-way quantum computation, quantum annealing andclassical annealing, and are described, for example, in Farhi, E. etal., “Quantum Adiabatic Evolution Algorithms versus Simulated Annealing”arXiv.org:quant-ph/0201031 (2002), pp 1-16.

Qubits

As mentioned previously, qubits can be used as fundamental units ofinformation for a quantum computer. As with bits in UTMs, qubits canrefer to at least two distinct quantities; a qubit can refer to theactual physical device in which information is stored, and it can alsorefer to the unit of information itself, abstracted away from itsphysical device. Examples of qubits include quantum particles, atoms,electrons, photons, ions, and the like.

Qubits generalize the concept of a classical digital bit. A classicalinformation storage device can encode two discrete states, typicallylabeled “0” and “1”. Physically these two discrete states arerepresented by two different and distinguishable physical states of theclassical information storage device, such as direction or magnitude ofmagnetic field, current, or voltage, where the quantity encoding the bitstate behaves according to the laws of classical physics. A qubit alsocontains two discrete physical states, which can also be labeled “0” and“1”. Physically these two discrete states are represented by twodifferent and distinguishable physical states of the quantum informationstorage device, such as direction or magnitude of magnetic field,current, or voltage, where the quantity encoding the bit state behavesaccording to the laws of quantum physics. If the physical quantity thatstores these states behaves quantum mechanically, the device canadditionally be placed in a superposition of 0 and 1. That is, the qubitcan exist in both a “0” and “1” state at the same time, and so canperform a computation on both states simultaneously. In general, Nqubits can be in a superposition of 2^(N) states. Quantum algorithmsmake use of the superposition property to speed up some computations.

In standard notation, the basis states of a qubit are referred to as the|0> and |1> states. During quantum computation, the state of a qubit, ingeneral, is a superposition of basis states so that the qubit has anonzero probability of occupying the |0> basis state and a simultaneousnonzero probability of occupying the |1> basis state. Mathematically, asuperposition of basis states means that the overall state of the qubit,which is denoted |Ψ>, has the form |Ψ>=a|0>+b|1), where a and b arecoefficients corresponding to the probabilities |a|² and |b|²,respectively. The coefficients a and b each have real and imaginarycomponents, which allows the phase of the qubit to be characterized. Thequantum nature of a qubit is largely derived from its ability to existin a coherent superposition of basis states and for the state of thequbit to have a phase. A qubit will retain this ability to exist as acoherent superposition of basis states when the qubit is sufficientlyisolated from sources of decoherence.

To complete a computation using a qubit, the state of the qubit ismeasured (i.e., read out). Typically, when a measurement of the qubit isperformed, the quantum nature of the qubit is temporarily lost and thesuperposition of basis states collapses to either the |0) basis state orthe |1) basis state and thus regaining its similarity to a conventionalbit. The actual state of the qubit after it has collapsed depends on theprobabilities |a|² and |b|² immediately prior to the readout operation.

Superconducting Qubits

There are many different hardware and software approaches underconsideration for use in quantum computers. One hardware approach usesintegrated circuits formed of superconducting materials, such asaluminum or niobium. The technologies and processes involved indesigning and fabricating superconducting integrated circuits aresimilar in some respects to those used for conventional integratedcircuits.

Superconducting qubits are a type of superconducting device that can beincluded in a superconducting integrated circuit. Typicalsuperconducting qubits, for example, have the advantage of scalabilityand are generally classified depending on the physical properties usedto encode information including, for example, charge and phase devices,phase or flux devices, hybrid devices, and the like. Superconductingqubits can be separated into several categories depending on thephysical property used to encode information. For example, they may beseparated into charge, flux and phase devices, as discussed in, forexample Makhlin et al., 2001, Reviews of Modern Physics 73, pp. 357-400.Charge devices store and manipulate information in the charge states ofthe device, where elementary charges consist of pairs of electronscalled Cooper pairs. A Cooper pair has a charge of 2e and consists oftwo electrons bound together by, for example, a phonon interaction. Seee.g., Nielsen and Chuang, Quantum Computation and Quantum Information,Cambridge University Press, Cambridge (2000), pp. 343-345. Flux devicesstore information in a variable related to the magnetic flux throughsome part of the device. Phase devices store information in a variablerelated to the difference in superconducting phase between two regionsof the phase device. Recently, hybrid devices using two or more ofcharge, flux and phase degrees of freedom have been developed. See e.g.,U.S. Pat. No. 6,838,694 and U.S. Pat. No. 7,335,909.

Examples of flux qubits that may be used include rf-SQUIDs, whichinclude a superconducting loop interrupted by one Josephson junction, ora compound junction (where a single Josephson junction is replaced bytwo parallel Josephson junctions), or persistent current qubits, whichinclude a superconducting loop interrupted by three Josephson junctions,and the like. See e.g., Mooij et al., 1999, Science 285, 1036; andOrlando et al., 1999, Phys. Rev. B 60, 15398. Other examples ofsuperconducting qubits can be found, for example, in Il'ichev et al.,2003, Phys. Rev. Lett. 91, 097906; Blatter et al., 2001, Phys. Rev. B63, 174511, and Friedman et al., 2000, Nature 406, 43. In addition,hybrid charge-phase qubits may also be used.

The qubits may include a corresponding local bias device. The local biasdevices may include a metal loop in proximity to a superconducting qubitthat provides an external flux bias to the qubit. The local bias devicemay also include a plurality of Josephson junctions. Eachsuperconducting qubit in the quantum processor may have a correspondinglocal bias device or there may be fewer local bias devices than qubits.In some embodiments, charge-based readout and local bias devices may beused. The readout device(s) may include a plurality of dc-SQUIDmagnetometers, each inductively connected to a different qubit within atopology. The readout device may provide a voltage or current. Thedc-SQUID magnetometers including a loop of superconducting materialinterrupted by at least one Josephson junction are well known in theart.

Effective Qubit

Throughout this specification and the appended claims, the terms“effective qubit” and “effective qubits” are used to denote a quantumsystem that may be represented as a two-level system. Those of skill inthe relevant art will appreciate that two specific levels may beisolated from a multi-level quantum system and used as an effectivequbit. Furthermore, the terms “effective qubit” and “effective qubits”are used to denote a quantum system comprising any number of devicesthat may be used to represent a single two-level system. For example, aplurality of individual qubits may be coupled together in such a waythat the entire set, or a portion thereof, of coupled qubits representsa single two-level system.

Quantum Processor

A computer processor may take the form of an analog processor, forinstance a quantum processor such as a superconducting quantumprocessor. A superconducting quantum processor may include a number ofqubits and associated local bias devices, for instance two or moresuperconducting qubits. Further detail and embodiments of exemplaryquantum processors that may be used in conjunction with the presentsystems, methods, and apparatus are described in US Patent PublicationNo. 2006-0225165, U.S. patent application Ser. No. 12/013,192, and U.S.Provisional Patent Application Ser. No. 60/986,554 filed Nov. 8, 2007and entitled “Systems, Devices and Methods for Analog Processing.”

A superconducting quantum processor may include a number of couplingdevices operable to selectively couple respective pairs of qubits.Examples of superconducting coupling devices include rf-SQUIDs anddc-SQUIDs, which couple qubits together by flux. SQUIDs include asuperconducting loop interrupted by one Josephson junction (an rf-SQUID)or two Josephson junctions (a dc-SQUID). The coupling devices may becapable of both ferromagnetic and anti-ferromagnetic coupling, dependingon how the coupling device is being utilized within the interconnectedtopology. In the case of flux coupling, ferromagnetic coupling impliesthat parallel fluxes are energetically favorable and anti-ferromagneticcoupling implies that anti-parallel fluxes are energetically favorable.Alternatively, charge-based coupling devices may also be used. Othercoupling devices can be found, for example, in US Patent Publication No.2006-0147154 and U.S. patent application Ser. No. 12/017,995. Respectivecoupling strengths of the coupling devices may be tuned between zero anda maximum value, for example, to provide ferromagnetic oranti-ferromagnetic coupling between qubits.

Quantum Annealing

Quantum annealing is a computation method that may be used to find alow-energy state, typically preferably the ground state, of a system.Similar in concept to classical annealing, the method relies on theunderlying principle that natural systems tend towards lower energystates because lower energy states are more stable. However, whileclassical annealing uses classical thermal fluctuations to guide asystem to its global energy minimum, quantum annealing may use naturalquantum fluctuations, such as quantum tunneling, to reach a globalenergy minimum more accurately or more quickly. It is known that thesolution to a hard problem, such as a combinatorial optimizationproblem, may be encoded in the ground state of a system and thereforequantum annealing may be used to find the solution to such hardproblems.

Adiabatic Quantum Computation

As mentioned previously, adiabatic quantum computation typicallyinvolves evolving a system from a known initial Hamiltonian (theHamiltonian being an operator whose eigenvalues are the allowed energiesof the system) to a final Hamiltonian by gradually changing theHamiltonian. A simple example of an adiabatic evolution is:

H _(e)=(1−s)H _(i) +sH _(f)

where H_(i) is the initial Hamiltonian, H_(f) is the final Hamiltonian,H_(e) is the evolution or instantaneous Hamiltonian, and s is anevolution coefficient which controls the rate of evolution. Thecoefficient s goes from 0 to 1, such that at the beginning of theevolution process the evolution Hamiltonian is equal to the initialHamiltonian and at the end of the process the evolution Hamiltonian isequal to the final Hamiltonian. If the evolution is too fast, then thesystem can be excited to a higher state, such as the first excitedstate. In the present systems, methods, and apparatus, an “adiabatic”evolution is considered to be an evolution that satisfies the adiabaticcondition, wherein the adiabatic condition is expressed as:

{dot over (s)}|<1|dH _(e) /ds|0>|=δg²(s)

where {dot over (s)} is the time derivative of s, g(s) is the differencein energy between the ground state and first excited state of the system(also referred to herein as the “gap size”) as a function of s, and δ isa coefficient much less than 1.

The evolution process in adiabatic quantum computing may sometimes bereferred to as annealing. The rate that s changes, sometimes referred toas an evolution or annealing schedule, is normally constant and slowenough that the system is always in the instantaneous ground state ofthe evolution Hamiltonian during the evolution, and transitions atanti-crossings (i.e., when the gap size is smallest) are avoided.Further details on adiabatic quantum computing systems, methods, andapparatus are described in U.S. Pat. No. 7,135,701.

Adiabatic quantum computation is a special case of quantum annealing forwhich the system begins and remains in its ground state throughout theevolution. Thus, those of skill in the art will appreciate that quantumannealing methods may generally be implemented on an adiabatic quantumcomputer, and vice versa. Throughout this specification, the term“adiabatic quantum computer” is used to describe a computing system thatis designed to perform adiabatic quantum computations and/or quantumannealing.

Optimization Problems

Optimization problems are problems for which one or more objectivefunctions are minimized or maximized over a set of variables, sometimessubject to a set of constraints. For example, the Traveling SalesmanProblem (“TSP”) is an optimization problem where an objective functionrepresenting, for example, distance or cost, must be optimized to findan itinerary, which is encoded in a set of variables representing theoptimized solution to the problem. For example, given a list oflocations, the problem may consist of finding the shortest route thatvisits all locations exactly once. Other examples of optimizationproblems include Maximum Independent Set (MIS), integer programming,constraint optimization, factoring, prediction modeling, and k-SAT.These problems are abstractions of many real-world optimizationproblems, such as operations research, financial portfolio selection,scheduling, supply management, circuit design, and travel routeoptimization. Many large-scale decision-based optimization problems areNP-hard. See e.g., “A High-Level Look at Optimization: Past, Present,and Future” e-Optimization.com, 2000.

Many optimization problems are not solvable using UTMs. Because of thislimitation, there is need in the art for computational devices capableof solving computational problems beyond the scope of UTMs. Classicaldigital computers are generally regarded as being unable to exceed thecapabilities of UTMs, and accordingly, are subject to the limits ofclassical computing that impose unfavorable scaling between problem sizeand solution time. In accordance with the present systems, methods andapparatus, quantum adiabatic algorithms may be employed to obtain bettersolutions to these problems than can be achieved with classicaloptimization algorithms.

Graph Embedding

Graphs are an effective way of representing relationships amongentities, and are commonly used in areas such as economics, mathematics,natural sciences and social sciences. While some graphs are simply usedas a visual aid, others can be used to represent a problem to be solved.In fact, mapping a problem into graph format can sometimes help solvethe problem. Instances of such problems include stock portfolioselection, microwave tower placement, delivery route optimization andother large-scale problems. Quantum computers can be used to solve suchproblems by way of translation of the original problem to a form thatthe quantum computer can solve. One method of doing this is throughgraph embedding, where a graph composed of a set of vertices and a setof edges that connect various vertices, representing a problem to besolved, is mapped into the qubit structure of a quantum processor andthen solved.

Graph embedding involves defining a particular drawing of a graph bymapping every node, or vertex, to a point on a plane and every edge to astraight or curved line that connects two nodes. This drawing is notunique, as there can be many permutations of the same graph. The numberof ways a graph can be embedded depends on the characteristics and rulesof the grid system upon which they are drawn. For example, one gridsystem can be a two-dimensional lattice. The edges may, for example, beconstrained to be in two mutually orthogonal directions (e.g., up-downor left-right). Such a grid system has a connectivity of 4, meaning thateach node can have at maximum four edges connected to it, the edgesgoing only in the directions mentioned above. A similar grid systemwherein edges can also extend diagonally (e.g., at 45°) and where theycan cross is of connectivity 8. One form of graph embedding involvestaking a graph drawn on one grid system and drawing an equivalent graphon another grid system.

Graphs that can be embedded can be broken into two types: planar andnon-planar. Planar graphs are graphs that can be embedded on atwo-dimensional plane such that no two edges intersect. A non-planargraph is a graph where at least two edges intersect. Some forms of graphembedding involve embedding a planar graph into a non-planar graph orattempting to make a non-planar graph as planar as possible, i.e., byreducing the number of intersections. However, some non-planar graphscannot be embedded into a planar graph. The most famous examples of suchgraphs are the graphs K5 and K(3, 3). More information on non-planargraphs and their embeddings can be found in Boyer et al., 2004, Journalof Graph Algorithms and Applications 8, pp. 241-273.

A technique of graph embedding into a lattice of qubits is described inKnysh et al., 2005, arXiv.org:quant-ph/0511131. Knysh describes atechnique of mapping NP-complete problems into a lattice of qubits andperforming adiabatic quantum computation to solve the problem. However,Knysh uses constant couplings between qubits and only nearest neighborcouplings, both of which reduce the flexibility and efficiency of theembedding and subsequent computation.

Further techniques of embedding graphs into a lattice of qubits aredescribed in U.S. patent application Ser. No. 11/932,248.

Relational Databases

Many entities employ relational databases to store information. Theinformation may be related to almost any aspect of business, governmentor individuals. For example, the information may be related to humanresources, transportation, order placement or picking, warehousing,distribution, budgeting, oil exploration, surveying, polling, images,geographic maps, network topologies, identification, and/or security.

There are many alternative techniques of searching databases, thoughmost approaches typically employ the preparation of one or more queries.For example, a technique is described in U.S. patent application Ser.No. 11/932,261, wherein a query is established in the form of a graphconsisting of nodes and edges. In this technique, the entries in thedatabase are used to generate database graphs, and each database graphis combined with the query graph to produce a set of association graphs.An association graph can then be used to evaluate the relation betweenthe query graph and the corresponding database graph. In certainembodiments, an association graph is embedded onto a quantum processorcomprising a set of qubits with the vertices of the association graphbeing represented by qubits and the edges of the association graph beingrepresented by coupling devices between qubits. The qubits and couplingdevices may be superconducting devices. The query corresponding to theassociation graph may be solved as a clique problem using the quantumprocessor. For example, the quantum processor may be evolved from afirst or “initial” state to a second or “final” state, with the finalstate being representative of an arbitrary clique of the associationgraph or alternatively, a maximal clique or a maximum clique of theassociation graph. In certain embodiments, the query is best fulfilledby the database graph whose corresponding association graph produces thelargest maximum clique.

Elastic Bunch Graph Matching

Elastic Bunch Graph Matching (EBGM) is a system for recognizing a singlehuman face in a database of many unique facial images. Specifically,EBGM is a process by which an image of a human face is analyzed and alabeled graph representation is generated. The labeled graphrepresentation is comprised of nodes and edges and is called an imagegraph. The nodes of the graph represent various “fiducial” points on theface (such as the eyes, nose, and mouth) and these nodes are weighted bysets of Gabor wavelet components called “jets.” The edges of the graphrepresent relationships between fiducial points and the edges arelabeled with two-dimensional distance vectors. Subsequent to theautomatic generation of an image graph representation by EBGM, facialrecognition may be accomplished by comparing the image graph of a queryimage with the respective image graphs of all images in a database.

The automatic generation of an image graph in EBGM is accomplished byaligning the facial image with a generalized “bunch” graph. The bunchgraph is essentially a model grid for which each individual fiducialpoint is labeled with a set (or “bunch”) of multiple jets rather thanwith one specific jet. The bunch graph overlays the facial image and thejet that best represents each fiducial point in the image is identified.The bunch graph therefore acts as a combinatorial entity, like amoldable mask. Edges in the bunch graph are sufficiently elastic thatthe resulting image graph may adapt to better fit the specific facialimage. Initially, a bunch graph is defined manually and it grows inadaptability and accuracy as more and more facial images areincorporated into the bunch. More detailed descriptions of the processof EBGM may be found in Wiskott et al., Face Recognition by ElasticBunch Graph Matching, IEEE Transactions on Pattern Analysis and MachineIntelligence, 19(7):775-779, 1997. An important point is that anincrease in the accuracy of EBGM demands an increase in computationaleffort. For example, better accuracy may be obtained by increasing thenumber of fiducial points in a bunch graph. However, such an increasewill demand greater computational effort in the EBGM image graphgeneration phase and lead to an image graph comprising a greater numberof nodes and edges. Such a larger image graph demands more computationaleffort during the recognition phase when it is compared to all otherimage graphs in a database. As such, current techniques for automaticfacial matching either do not produce the desired level of accuracy orthey are too slow.

The problem of image matching is particularly well-suited to be solvedon such quantum processors. Techniques of image recognition that arecurrently in practice are limited in their accuracy and are generallyquite slow. Recognition accuracy depends on the accuracy of the graphrepresentation, which itself ultimately depends on the number of imagefeatures identified. Traditionally, attempts to incorporate greaternumbers of image features result in graph representations that arecomputationally exhaustive in the recognition process. Thus, somemeasure of accuracy is typically compromised to accommodate manageablecomputation times. By performing the recognition process on a quantumprocessor, recognition may be obtained with greater accuracy and/or morequickly than traditional methods.

BRIEF SUMMARY

At least one embodiment may be summarized as a computer-implementedmethod of identifying features of query images in a database of images,including comparing a graph representation of at least one feature of aquery image to a respective graph representation of at least a portionof each of at least some of a plurality of database images of a databaseof images, wherein each comparison includes generating a respectiveassociation graph; and determining at least one characteristic of eachassociation graph via a quantum processor, wherein the at least onecharacteristic of each association graph is representative of asimilarity between the at least one feature of the query image and atleast the portion of the respective database image to which theassociation graph corresponds.

The method may further include storing a result from the determining atleast one characteristic of each association graph; and ranking theresults such that the highest ranking result represents the most likelymatch between the feature of the query image and at least one of thedatabase images. At least some of the plurality of database images mayeach include data representative of at least one human face, and whereinthe feature of the query image may include data representative of atleast one human face. The method may further include generating therespective graph representation of at least the portion of each of atleast some of the database images of the database of images; andgenerating the graph representation of the at least one feature of thequery image. Generating graph representations of at least the portion ofeach of at least some of the database image and of the at least onefeature of the query image may include performing Elastic Bunch GraphMatching. Generating the respective graph representations of at leastthe portion of each database image may include generating the respectivegraph representations using a classical digital processor. Generatingthe graph representation of the at least one feature of the query imagemay include generating the graph representation using a classicaldigital processor. Determining at least one characteristic of eachassociation graph may include determining a maximum independent set ofeach association graph. Determining at least one characteristic of eachassociation graph may include determining a maximum clique of eachassociation graph. Determining at least one characteristic of eachassociation graph via a quantum processor may include determining atleast one characteristic of each association graph via a superconductingquantum processor that comprises a plurality of superconducting qubits.The method may further include accessing the database of images via aclassical digital processor. Generating the respective associationgraphs may include generating the respective associating graphs using aclassical digital processor. The method may further include transmittingthe respective association graphs from the classical digital processorto the quantum processor. The method may further include transmittingthe at least one characteristic of each association graph that isdetermined by the quantum processor from the quantum processor to theclassical digital processor. The method may further include examining atleast a portion of the query image prior to comparing the graphrepresentation of the query image with the graph representations of thedatabase images; and identifying an aspect of the query image that iscommon to a subset of the database images, and wherein comparing a graphrepresentation of the at least one feature of a query image to arespective graph representation of each of at least some of a pluralityof database images may include comparing the graph representation of theat least one feature of the query image to only the graph representationof the databases images in the subset of the database images, withcorresponding association graphs being produced therefor. The at leastone feature of the query image may represent a majority of the queryimage. The similarity between the feature of the query image and the atleast a portion of the respective database image to which theassociation graph corresponds may be indicative of whether or not the atleast one feature of the query image occurs within the respectivedatabase image to which the association graph corresponds.

At least one embodiment may be summarized as a computer-implementedmethod of solving image matching problems, including casting an imagematching problem as a quadratic unconstrained binary optimizationproblem; mapping the quadratic unconstrained binary optimization problemto a quantum processor; and evolving the quantum processor to produce asolution to the quadratic unconstrained binary optimization problem.

At least one embodiment may be summarized as a computer-implementedmethod of comparing two objects, including comparing a graphrepresentation of at least a portion of a first object to a graphrepresentation of at least a portion of a second object, wherein thecomparison includes generating an association graph; and determining atleast one characteristic of the association graph via a quantumprocessor, wherein the at least one characteristic of the associationgraph is representative of a similarity between the at least a portionof the first object and the at least a portion of the second object.

The method may further include the first object and the second objectboth being images. Determining at least one characteristic of theassociation graph may include determining a maximum independent set ofthe association graph. Determining at least one characteristic of theassociation graph may include determining a maximum clique of theassociation graph. Determining at least one characteristic of theassociation graph may result in the quantum processor returning a valuethat is representative of a measure of similarity between the at least aportion of the first object and the at least a portion of the secondobject.

BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWING(S)

In the drawings, identical reference numbers identify similar elementsor acts. The sizes and relative positions of elements in the drawingsare not necessarily drawn to scale. For example, the shapes of variouselements and angles are not drawn to scale, and some of these elementsare arbitrarily enlarged and positioned to improve drawing legibility.Further, the particular shapes of the elements as drawn are not intendedto convey any information regarding the actual shape of the particularelements, and have been solely selected for ease of recognition in thedrawings.

FIG. 1 is a flow-diagram of an embodiment of a method for performingautomatic image recognition with a system comprising a quantumprocessor.

FIG. 2A is an illustrative diagram showing a graph representation of afacial image overlaying the facial image itself.

FIG. 2B is a flow-diagram of an embodiment of a method for communicatinga problem from a classical processor to a quantum processor.

FIG. 3 is a schematic diagram of a portion of a conventionalsuperconducting quantum processor designed for adiabatic quantumcomputation (and/or quantum annealing).

FIG. 4 is a flow-diagram of an embodiment of a method for a native modeof operation in solving an image matching problem with a quantumprocessor.

FIG. 5 is a flow-diagram of an embodiment of a method for a hybrid modeof operation in solving an image matching problem with a quantumprocessor.

DETAILED DESCRIPTION

In the following description, certain specific details are set forth inorder to provide a thorough understanding of various disclosedembodiments. However, one skilled in the relevant art will recognizethat embodiments may be practiced without one or more of these specificdetails, or with other methods, components, materials, etc. In otherinstances, well-known structures associated with analog processors, suchas quantum processors, quantum devices, coupling devices and controlsystems including microprocessors and drive circuitry have not beenshown or described in detail to avoid unnecessarily obscuringdescriptions of the embodiments.

Unless the context requires otherwise, throughout the specification andclaims which follow, the word “comprise” and variations thereof, suchas, “comprises” and “comprising” are to be construed in an open,inclusive sense, that is, as “including, but not limited to.”

Reference throughout this specification to “one embodiment” or “anembodiment” means that a particular feature, structure or characteristicdescribed in connection with the embodiment is included in at least oneembodiment. Thus, the appearances of the phrases “in one embodiment” or“in an embodiment” in various places throughout this specification arenot necessarily all referring to the same embodiment. Further more, theparticular features, structures, or characteristics may be combined inany suitable manner in one or more embodiments.

As used in this specification and the appended claims, the singularforms “a,” “an,” and “the” include plural referents unless the contentclearly dictates otherwise. It should also be noted that the term “or”is generally employed in its sense including “and/or” unless the contentclearly dictates otherwise.

The headings and Abstract of the Disclosure provided herein are forconvenience only and do not interpret the scope or meaning of theembodiments.

The present systems, methods, and apparatus describe techniques forimplementing a quantum processor to perform automatic image recognitionin a database of images. In order to do this, an image matching problemis mapped to a form that may be processed by a quantum processor. Imagesmay take a variety of form. Typically, images take the form of digitalinformation that can be used to produce a visual representation of theimage, for instance on a display or on paper. The image may, forexample, take the form of information that defines a bit map, forinstance specifying intensities and/or colors for various pixels of atwo dimensional array. Also for example, the image may take the form ofa mathematical representation, for example one or more polynomialexpressions (e.g., B-Spline polynomials) or vectors. Images may takeother forms as well.

Image matching in its simplest form attempts to find pairs of imagefeatures from two images that correspond to the same physical structure.An image feature may, for example, include a vector that describes theneighborhood of a given image location. In order to find correspondingfeatures, two factors are typically considered: feature similarity, asfor instance determined by the scalar product between feature vectors,and geometric consistency. This latter factor is best defined whenlooking at rigid objects. In this case the feature displacements are notrandom but rather exhibit correlations brought about by a change inviewpoint. For instance, if the camera moves to the left, translation ofthe feature locations in the image to the right may be observed. If theobject is deformable or articulatable then the feature displacements arenot solely determined by the camera viewpoint, but neighboring featuresmay still tend to move in a similar way. Thus, image matching can becast as an optimization problem involving the minimization of anobjective function that consists of at least two terms. The first termpenalizes mismatches between features drawn from a first image andplaced at corresponding locations in a second image. The second termenforces spatial consistency between neighboring matches by measuringthe divergence between them. It has been shown in Felzenzwalb &Huttenlocher, “Pictorial Structures for Object Recognition,” Intl.Journal of Computer Visions 61(1), 55-79 (2005) that this constitutes anNP-hard optimization problem.

In order to make an image matching problem amenable to a solution with aquantum algorithm, the image matching problem may be mapped to aquadratic unconstrained binary optimization (“QUBO”) problem of theform:

$\begin{matrix}{{{\overset{->}{x}}_{opt} = {\arg \; \min \left\{ {\sum\limits_{{i \leq j} = 1}^{N}\; {Q_{ij}x_{i}x_{j}}} \right\}}},{x_{i}ɛ\left\{ {0,1} \right\}}} & (1)\end{matrix}$

The binary optimization variables x_(i), x_(j) determine how features inone image map to features in another image. The coefficients Q_(ij) arechosen so that minimization of the resultant objective functionmaximizes both feature similarity and geometric consistency. Equation(1) may be solved using a quantum computing algorithm, such as a quantumadiabatic algorithm.

A general method for implementing a quantum processor to solve the imagematching problem is now provided. FIG. 1 is a flow-diagram thatillustrates an embodiment of this method 100. Method 100 is a novelcombination of three acts: generating graph representations of images101 and 102 (e.g., electronic data or information representing visualimages), pattern matching using association graphs 103, and solving aproblem 104 using a system including a quantum processor. In act 101,graph representations of some or all of the images (“database images”)in a database of images (“database graphs”) are established. This may bedone, for example, using a conventional (digital) processor. In act 102,a graph representation of a query image (“query graph”) is established.In act 103, the query graph is compared to the database graphs and, foreach comparison, a corresponding association graph is generated. In act104, at least one characteristic of each association graph is determinedusing a quantum processor. In act 105, the results are ranked accordingto the at least one characteristic of the association graphs asdetermined by the quantum processor. The ranking may be established suchthat the highest ranking indicates the most likely match between thequery graph and the corresponding database graph and hence between thequery image and the corresponding database image.

In act 104, the characteristic or characteristics of the associationgraphs that may be determined by a quantum processor may depend on thetype of images being examined or on the nature of recognition algorithm.Two appropriate characteristics include the Maximum Independent Set(“MIS”) and the Maximum Clique (“MC”) of the association graphs. Thesetwo characteristics are related and, as such, image recognition may beperformed by determining only one of these two characteristics in eachassociation graph. The MIS of a graph is the largest subset of nodesthat are all connected by edges. A larger MIS in an association graphindicates a better match between the query graph and the correspondingdatabase graph. Thus, the association graph that is determined to havethe largest MIS is expected to correspond to the most likely matchbetween the query image and a database image. As an alternative to MIS,MC is the largest subset of nodes that do not share any edges, andtherefore the association graph with the largest MIS will typically havethe smallest MC. Thus, those of skill in the relevant art willappreciate that solving an MC problem is analogous to solving an MISproblem, the only difference being that the ranking order is inverted.Method 100 may be implemented to enhance the speed and/or the accuracyof automatic image recognition over the techniques that are currently inpractice.

Method 100 may be applied to find a database image that matches a queryimage. However, method 100 may also be applied to find a database imagethat includes a specific feature that matches a specific feature that isincluded in a query image. The distinction here is that, in addition tomatching whole images, method 100 may be applied to identify a featurein a query image and find a match to that feature in a database ofimages. For example, a query image may include a human face, and method100 may be applied to find, within a database of images, a databaseimage that includes a matching human face, even if the resultingdatabase image includes a plurality of human faces where the matchingface is only one feature of the database image. In such applications,some embodiments of method 100 may provide that the graph representationof the query image established in act 102 be limited to a graphrepresentation of the specific feature of the query image for which amatch is sought.

The present systems, methods, and apparatus describe the use of both adigital processor and a quantum processor in performing automatic imagerecognition. In some embodiments, the generation of graphrepresentations of images (or specific features of images, depending onthe desired query) and the generation of association graphs may beperformed using a digital processor, while the determination of at leastone characteristic of each association graph may be performed using aquantum processor.

Facial images are specific examples of a type of image that may berepresented by graphs. The generation of graph representations of facialimages is a field of study that continues to evolve and grow. The basicprinciple is that the relative positions of specific features on theface (such as the eyes, nose, and mouth, as well as many other moresubtle features) may ultimately define a combination that is unique foreach face. Thus, a graph representation of these relative positions maybe used to identify an individual in much the same way as a fingerprint.In such a graph representation, the identifiable features (again, suchas the eyes and mouth) may be represented by nodes or vertices that areconnected by a web of edges. The edges may define the relative positionsof the nodes. The greater the number of nodes (that is, the greater thenumber of features that are identified on an image) the better theaccuracy of the graph representation. An identical or similar approachmay be taken with respect to images that are representative of otherbody parts, for example iris or fingerprints.

FIG. 2A is an illustrative diagram showing a graph representation 200overlaying an original facial image. In FIG. 2A, nodes 201-204 definethe outline of the mouth. For the sake of simplicity, graphrepresentation 200 is made up of relatively few nodes (only four calledout in the Figure) and is therefore a relatively inaccuraterepresentation of the original facial image. However, those of ordinaryskill in the art will appreciate that the accuracy of a graphrepresentation of a facial image may be improved by increasing thenumber of nodes in the graph and thus representing more facial featuresin the image. Furthermore, FIG. 2A is meant to serve only as anillustrative example of a graph representation of a facial image. Thespecific facial features that are identified with nodes in FIG. 2A, andthe corresponding edges between nodes, do not represent a required graphscheme. Those of skill in the art will appreciate that the specificfacial features that are identified in a graph representation, as wellas the corresponding network of edges between nodes, may vary accordingto the method by which the graph representation is generated. Those ofskill in the art will also appreciate that the principles and techniquesof generating graph representations of facial images may be applied toother image types, such as images of objects, landscapes, maps,fingerprints, etc. Thus, while FIG. 2A shows a graph representation of afacial image only, those of skill in the art will appreciate how graphrepresentations of any type of images may similarly be established.

A graph representation of an image may be drawn manually, or it may begenerated automatically. The ultimate goal of such graph representationsis in image recognition, which may require that graph representations beestablished for every image in a very large database of images. As such,it is more practical to develop a system for automatically generatinggraph representations of images rather than drawing all by hand. Anexample of such a system is Elastic Bunch Graph Matching (EBGM). EBGM isspecifically designed to be applied to facial images; however, the basicprinciples may be applied to images of any type. In EBGM, generalizedmodel graphs are established which are then fit to new facial images andmolded to create new graphs. The full details of this technique aredescribed in Wiskott et al., Face Recognition by Elastic Bunch GraphMatching, IEEE Transactions on Pattern Analysis and MachineIntelligence, 19(7):775-779, 1997. A continuing challenge of thistechnique is the trade-off between accuracy and speed, since increasingthe accuracy of a graph representation results in increasedcomputational effort during the recognition process. However, byincorporating pattern matching using association graphs and then using aquantum processor to solve the resulting MIS problem, both accuracy andcomputation time may be improved beyond the techniques that arecurrently in practice.

EBGM is a leading technique in the automatic generation of graphrepresentations of facial images. However, those of skill in the artwill appreciate that the present systems, methods, and apparatus do notrequire that the graph representations be generated by EBGM. Aspreviously discussed, the graph representations of facial images, or anyother image type, may be generated manually or by using any othersystem, as long as there is enough consistency among the query anddatabase graphs that meaningful association graphs may be generated.

For certain queries, it may be desirable to use a classical digitalprocessor to identify certain key aspects of the query image that areautomatically indicative of a certain subset in the database. Forinstance, while the graph representation of the query image is beinggenerated, or from the graph representation before the association graphis generated, it may be possible to identify some aspect of the queryimage that immediately relates the query to some subset in the database.When such an identification is made, the query image need only becompared against those database images that share the same aspect andtherefore fewer association graphs may be generated. Essentially, thedatabase is filtered or pruned so that only those images that stand achance of being recognized as a match are compared to produceassociation graphs. As an example, a query image may be initiallycategorized as relating to a human face, and a corresponding database ofimages may then be reduced to the subset of images that include at leastone human face. Furthermore, in facial image recognition it may bepossible to identify the race or sex of the facial image from the graphrepresentation of the query image prior to comparison with the databaseimages. In this example, the database to be examined would then bereduced to the subset of facial images that match the race or sex of thequery image. This would require fewer association graphs to begenerated, resulting in fewer calls to a quantum processor and reducedcomputation time. This preliminary filtering, or pruning, may beperformed by a user or by the digital computer.

Those of skill in the relevant art will appreciate that a graphrepresentation may be generated for any type of image. For example,images of objects, landscapes, maps, fingerprints, and constellationscan all be represented by graphs. Furthermore, a graph representationmay be generated for a specific feature of aspect of an image, ratherthan for the image as a whole.

Throughout this specification and the appended claims, reference is madeto communication between a classical processor and a quantum processor.For instance, association graphs may be generated using a classicalprocessor as in act 103 of method 100, and a quantum processor may thenbe used to analyze the association graphs as in act 104 of method 100.FIG. 2B is a flow-diagram that illustrates an embodiment of a method 250for communicating between a classical processor and a quantum processor.Method 250 includes four acts, 251-254. In act 251, a query is processedusing a classical processor. The processing of a query may include avariety of actions, including but not limited to defining the parametersof a query, identifying a specific feature in a query image, generatingassociation graphs, classifying a query, and establishing exit criteria.The processing of the query may also include converting the query into aform that may be transmitted to and managed by a quantum processor. Inact 252, the processed query is transmitted from the classical processorto a quantum processor. In act 253, the quantum processor is used tosatisfy the query. Satisfying a query may include a variety ofprocesses, including but not limited to determining at least one feature(such as an MIS or MC) of an association graph. The quantum processormanages the query until the query is satisfied. In act 254, the resultof satisfying the query is returned to the classical processor. This mayinclude transmitting a result to the query from the quantum processor toa classical processor.

In accordance with the present systems, methods and apparatus,algorithms of adiabatic quantum computation and/or quantum annealing maybe implemented in a heuristic fashion, wherein the requirement forglobal optimality in the solution is dropped. Using such algorithms, aquantum processor may provide: a) a more accurate solution in the sameamount of time as a classical solving system, b) the same degree ofaccuracy in a shorter period of time than a classical solving system, orc) a more accurate solution in a shorter period of time than a classicalsolving system.

Adiabatic quantum computation, and similarly quantum annealing, may beimplemented in a variety of different ways. Examples of particularimplementations of adiabatic quantum computation are described in U.S.patent application Ser. No. 11/317,838 and Wocjan et al., 2003,“Treating the Independent Set Problem by 2D Ising Interactions withAdiabatic Quantum Computing,” arXiv.org: quant-ph/0302027 (2003), pp.1-13, where the qubit-coupling architecture is used to realize a 2-localIsing Hamiltonian with 1-local transverse field as given in equation 2:

$\begin{matrix}{H = {{\sum\limits_{i = 1}^{n}\; {h_{i}\sigma_{i}^{z}}} + {\sum\limits_{i = 1}^{n}\; {\Delta_{i}\sigma_{i}^{x}}} + {\sum\limits_{i,{j = 1}}^{n}\; {J_{ij}\sigma_{i}^{z}\sigma_{j}^{z}}}}} & (2)\end{matrix}$

Here, n represents the number of qubits, σ_(i) ^(z) is the PauliZ-matrix for the i^(th) qubit, σ_(i) ^(x) is the Pauli X-matrix for thei^(th) qubit, and h_(i), Δ_(i) and J_(ij) are dimensionless local fieldscoupled to each qubit. The h_(i) terms in equation 2 may be physicallyrealized by coupling signals or fields to the Z-basis of each i^(th)qubit. The Δ_(i) terms in equation 2 may be physically realized bycoupling signals or fields to the X-basis of each i^(th) qubit. TheJ_(ij) terms in equation 2 may be physically realized by coupling theZ-bases of pairs of qubits (qubits i and j, respectively) together.

FIG. 3 is a schematic diagram of a portion of a conventionalsuperconducting quantum processor 300 designed for adiabatic quantumcomputation (and/or quantum annealing). The portion of superconductingquantum processor 300 shown in FIG. 3 includes two superconductingqubits 301, 302 and a tunable ZZ-coupler 311 coupling informationtherebetween. While the portion of quantum processor 300 shown in FIG. 3includes only two qubits 301, 302 and one coupler 311, those of skill inthe art will appreciate that quantum processor 300 may include anynumber of qubits, and any number of coupling devices couplinginformation therebetween.

The portion of quantum processor 300 shown in FIG. 3 may be implementedto physically realize the Hamiltonian described by equation 2. In orderto provide the σ^(z) and σ^(x) terms, quantum processor 300 includesprogramming interfaces 321-324 that are used to configure and controlthe state of quantum processor 300. Each of programming interfaces321-324 may be realized by a respective inductive coupling, asillustrated, to a programming system (not shown). Such a programmingsystem may be separate from quantum processor 300, or it may be includedlocally (i.e., on-chip with quantum processor 300) as described in U.S.patent application Ser. No. 11/950,276.

In the programming of quantum processor 300, programming interfaces 321and 324 may each be used to couple a flux signal into a respectivecompound Josephson junction 331, 332 of qubits 301 and 302, therebyrealizing the Δ_(i) terms in the system Hamiltonian. This couplingprovides the σ^(x) terms of equation 2. Similarly, programminginterfaces 322 and 323 may each be used to couple a flux signal into arespective qubit loop of qubits 301 and 302, thereby realizing the h_(i)terms in the system Hamiltonian. This coupling provides the σ^(z) termsof equation 2. In FIG. 3, the contribution of each of programminginterfaces 321-324 to the system Hamiltonian is indicated in boxes 321a-324 a, respectively.

Those of skill in the art will appreciate that adiabatic quantumcomputation and/or quantum annealing may be achieved by implementingsystems that differ from system 300 in FIG. 3, and/or by implementingHamiltonians that differ from equation 2. System 300 and Hamiltonian 2are intended to serve only as examples of embodiments of the presentsystems, methods and apparatus.

The present systems, methods and apparatus provide at least two modes ofusing a quantum processor to solve the image matching problem, where thepreferred mode depends on the size of the problem (i.e., the number ofvertices in the association graphs). In a first mode of operation, the“native mode”, the problem size is small enough that the entire problemmay be mapped directly to the quantum processor. In a second mode ofoperation, the “hybrid mode”, the problem size is too large to be mappeddirectly to the quantum processor and, to compensate, the problem isdecomposed into a set of smaller problems that may be mappedindividually to the quantum processor.

In native mode operation, the image matching problem is mapped directlyto the quantum processor. For any pair of images (i.e., a query imageplus a database image) an association graph may be used to measure thesimilarity between the graph representations of the two images. Eachvertex in an association graph may correspond to an association betweena feature a in a first image and a feature β in a second image. Eachedge in an association graph may encode some degree of geometricconsistency between a pair of feature vectors in a first image and apair of feature vectors in a second image. The MIS of an associationgraph provides both a similarity measure (the larger the MIS, thegreater the region of mutual overlap) and the largest conflict-freemapping of features in the first image to features in the second image.As previously discussed, this technique may be used to match two wholeimages, or to find a specific feature from a query image in among a setof database images. For example, a “match” may be provided if all or aportion of a query image is contained somewhere within a correspondingdatabase image. In accordance with the present systems, methods andapparatus, the problem of finding the MIS of an association graph may becast as a QUBO problem by setting Q_(ii)=−1 for all vertices andQ_(ij)=L whenever there is an edge between vertices. The minimum energyconfiguration of the QUBO problem enforces x_(i)=1 if and only if thecorresponding vertex is an element of the MIS, otherwise x_(i)=0.

FIG. 4 is a flow-diagram of an embodiment of a method 400 for a nativemode of operation in solving an image matching problem with a quantumprocessor. Method 400 provides more detail of the general methoddescribed by method 100 from FIG. 1. Specifically, method 400 providesan example of the acts used to perform act 104 of method 100 using aquantum processor similar to system 300 from FIG. 3 and implementing theHamiltonian described by equation 2. In act 104 of method 100, a quantumprocessor is used to determine at least one characteristic of anassociation graph. Accordingly, in act 401 of method 400, theassociation graph is defined as a matrix Q describing a connectedn-vertex QUBO, where n is limited by the number of qubits, or effectivequbits, in the quantum processor. In act 402, the target values of h_(i)and J_(ij) from equation 2 are determined from the matrix Q. In act 403,each of the n vertices is identified with a respective qubit, oreffective qubit, in the quantum processor. In act 404, a quantumalgorithm is implemented by the quantum processor. This algorithm mayinclude adiabatic quantum computation and/or quantum annealing by theapplication of appropriate time-dependent functions h_(i)(t), Δ_(i)(t)and J_(ij)(t). In act 405, the results of the quantum algorithm areevaluated. If the solution is not satisfactory then the method returnsto act 404. If the solution is satisfactory then the method proceeds toact 406. In act 406, the solution to the image matching problem isoutput.

Method 400 described in FIG. 4 provides a procedure for determining theMIS (or, alternatively, the MC) of a single association graph. Asdescribed in method 100 of FIG. 1, in an image matching problem a set ofassociation graphs may be generated, where each association graphcorresponds to a respective comparison between the query image and aunique database image. Method 400 effectively provides a procedure fordetermining how good a match is achieved between the query image and asingle database image. Thus, to solve an image matching problem it maybe necessary to complete method 400 for each association graph and thento rank the results as in act 105 of method 100.

For many adiabatic quantum computing architectures, the number ofphysical qubits available is likely to be much less than the number ofvariables in the image matching problem to be solved (i.e., n>the numberof qubits). Therefore, it may be necessary to decompose a large imagematching problem into a set of smaller problems. In such instances, itmay be necessary to implement a hybrid mode of operation where thecomplete image matching problem is decomposed into a set of smallerproblems such that each of the smaller problems may be solved by thequantum processor. Those of skill in the art will appreciate that a widevariety of decomposition techniques may be implemented for this purpose.The present systems, methods and apparatus describe techniques for usingthe quantum processor to perform this decomposition by implementing alocal search algorithm.

FIG. 5 is a flow-diagram of an embodiment of a method 500 for a hybridmode of operation in solving an image matching problem with a quantumprocessor. Similar to method 400 of FIG. 4, the goal of method 500 is tosolve a QUBO problem, where the solution represents an MIS (or,alternatively, an MC) of an association graph. In act 501, an initialapproximation of the solution is established using, for example, aclassical heuristic solver. An example of an appropriate classicalheuristic solver for QUBO problems is the Digest-Devour-Tidyup algorithmdescribed in Glover et al., “One pass heuristics for large scaleunconstrained binary quadratic problems,” University of MississippiTechnical Report HCES-09-00 (2000), available athttp://hces.bus.olemiss.edu/reports/hces0900.pdf, though those of skillin the art will appreciate that other classical heuristic solvers mayalternatively be used. The initial approximation of the solution is usedas the starting point of a local search algorithm. The initialapproximation of the solution includes a set of variables X_(o). In act502, a local search algorithm is initiated by selecting a subset S_(o)of the set of variables X_(o). The number of variables in the subsetS_(o) is less than or equal to the number of variables that can bemapped directly to the quantum processor. In act 503, the subset ofvariables S_(o) is mapped to the quantum processor as the optimizationproblem described in equation 3:

X_(S_(o))^(*) = arg  min_(X_(S_(o)))(X_(S_(o)), X_(∖S_(o)) = X_(∖S_(o)))

Thus, in act 503 the quantum processor is used to optimize the subset ofvariables S_(o) to improve the initial approximation of the solution. Inact 504, the improved solution determined in act 503 is re-cast as theinitial approximation of the solution. In act 505, acts 502-504 arereiterated until some exit criteria are met. Examples of suitable exitcriteria include, but are not limited to, a specified number ofiterations, a specified amount of time, and/or a specified degree ofaccuracy. In act 506, the final solution to the problem is output. Arecursive technique for quantum computation is described in U.S.Provisional Patent Application Ser. No. 60/943,519, filed Jun. 12, 2007and entitled “Systems, Methods, and Apparatus for Recursive QuantumComputing Algorithms.”

A potential disadvantage of method 500 is that it may only locate alocal minimum within the space of the subset of variables S_(o), ratherthan a global minimum in the space of all variables X_(o). In accordancewith the present systems, methods and apparatus, the local searchalgorithm of method 500 may be implemented in a tabu search heuristic toassist in escaping local minima. Each iteration of a tabu search (as isknown in the art) stores and recalls the results of previous iterations.Thus, in some embodiments, as method 500 is implemented the results fromeach iteration may be stored. These stored results may include datarelating to the effects of changing each single variable, therebyassociating a cost with changing each variable. In each successiveiteration, the algorithm may select a to adjust a variable that has notyet been changed, thereby producing a new entry in the stored data. Thisstored data then provides insight into the gradient of the solutionlandscape such that subsequent iterations may move towards the “best”local minima or, ideally, the global minimum.

Those of skill in the art will appreciate that through thisspecification the term “solve” is used to encompass both exact solutionsand approximate solutions.

As described, the present systems, methods and apparatus may be used forimage matching. This application may include matching two whole images,or it may include finding, within a database of images, a database imagethat contains all or a portion of a query image. For example, a queryimage may contain a road sign and it may be desired to find, within adatabase of images, a database image that includes a matching road signsomewhere therein. However, the concepts taught in the present systems,methods and apparatus may be applied to a much broader set of problems.A wide range of applications exist for which it is desirable to find amatch to a query within a database. In some embodiments, the presentsystems, methods and apparatus may be generalized as a method ofdetermining a measure of similarity between two objects, where featuresof the two objects are combined into an association graph that isanalyzed by a quantum processor. The quantum processor may analyze theassociation graph and return a value that is indicative of a measure ofsimilarity between the two objects. In some applications, the twoobjects may be images, such as a query image and a database image.However, in other applications, the two objects may take on other forms.For example, some embodiments may provide matching a query among theentries in a relational database. Other embodiments may provide patternmatching in other forms, such as but not limited to audio patternmatching, DNA sequence matching, and so on.

The above description of illustrated embodiments, including what isdescribed in the Abstract, is not intended to be exhaustive or to limitthe embodiments to the precise forms disclosed. Although specificembodiments of and examples are described herein for illustrativepurposes, various equivalent modifications can be made without departingfrom the spirit and scope of the disclosure, as will be recognized bythose skilled in the relevant art. The teachings provided herein of thevarious embodiments can be applied to other systems, methods andapparatus of quantum computation, not necessarily the exemplary systems,methods and apparatus for quantum computation generally described above.

The various embodiments described above can be combined to providefurther embodiments. All of the U.S. patents, U.S. patent applicationpublications, U.S. patent applications, foreign patents, foreign patentapplications and non-patent publications referred to in thisspecification and/or listed in the Application Data Sheet, including butnot limited to U.S. Provisional Patent Application Ser. No. 60/912,904,filed Apr. 19, 2007, entitled “Systems, Methods and Apparatus forAutomatic Image Recognition,” U.S. Pat. No. 6,838,694, U.S. Pat. No.7,335,909, US Patent Publication No. 2006-0225165, U.S. patentapplication Ser. No. 12/013,192, U.S. Provisional Patent ApplicationSer. No. 60/986,554 filed Nov. 8, 2007 and entitled “Systems, Devicesand Methods for Analog Processing”, US Patent Publication No.2006-0147154, U.S. patent application Ser. No. 12/017,995, U.S. Pat. No.7,135,701, U.S. patent application Ser. No. 11/932,248, U.S. patentapplication Ser. No. 11/932,261, U.S. patent application Ser. No.11/317,838, U.S. patent application Ser. No. 11/950,276, and U.S.Provisional Patent Application Ser. No. 60/943,519, filed Jun. 12, 2007and entitled “Systems, Methods, and Apparatus for Recursive QuantumComputing Algorithms” are incorporated herein by reference, in theirentirety. Aspects of the embodiments can be modified, if necessary, toemploy systems, circuits and concepts of the various patents,applications and publications to provide yet further embodiments.

These and other changes can be made to the embodiments in light of theabove-detailed description. In general, in the following claims, theterms used should not be construed to limit the claims to the specificembodiments disclosed in the specification and the claims, but should beconstrued to include all possible embodiments along with the full scopeof equivalents to which such claims are entitled. Accordingly, theclaims are not limited by the disclosure.

1. A computer-implemented method of identifying features of query imagesin a database of images, the method comprising: comparing a graphrepresentation of at least one feature of a query image to a respectivegraph representation of at least a portion of each of at least some of aplurality of database images of a database of images, wherein eachcomparison includes generating a respective association graph; anddetermining at least one characteristic of each association graph via aquantum processor, wherein the at least one characteristic of eachassociation graph is representative of a similarity between the at leastone feature of the query image and at least the portion of therespective database image to which the association graph corresponds. 2.The method of claim 1, further comprising: storing a result from thedetermining at least one characteristic of each association graph; andranking the results such that the highest ranking result represents themost likely match between the feature of the query image and at leastone of the database images.
 3. The method of claim 1 wherein at leastsome of the plurality of database images each include datarepresentative of at least one human face, and wherein the feature ofthe query image includes data representative of at least one human face.4. The method of claim 1, further comprising: generating the respectivegraph representation of at least the portion of each of at least some ofthe database images of the database of images; and generating the graphrepresentation of the at least one feature of the query image.
 5. Themethod of claim 4 wherein generating graph representations of at leastthe portion of each of at least some of the database image and of the atleast one feature of the query image includes performing Elastic BunchGraph Matching.
 6. The method of claim 4 wherein generating therespective graph representations of at least the portion of eachdatabase image includes generating the respective graph representationsusing a classical digital processor.
 7. The method of claim 4, andwherein generating the graph representation of the at least one featureof the query image includes generating the graph representation using aclassical digital processor.
 8. The method of claim 1 whereindetermining at least one characteristic of each association graphincludes determining a maximum independent set of each associationgraph.
 9. The method of claim 1 wherein determining at least onecharacteristic of each association graph includes determining a maximumclique of each association graph.
 10. The method of claim 1 whereindetermining at least one characteristic of each association graph via aquantum processor includes determining at least one characteristic ofeach association graph via a superconducting quantum processor thatcomprises a plurality of superconducting qubits.
 11. The method of claim1, further comprising: accessing the database of images via a classicaldigital processor.
 12. The method of claim 1 wherein generating therespective association graphs includes generating the respectiveassociating graphs using a classical digital processor.
 13. The methodof claim 10, further comprising: transmitting the respective associationgraphs from the classical digital processor to the quantum processor.14. The method of claim 13, further comprising: transmitting the atleast one characteristic of each association graph that is determined bythe quantum processor from the quantum processor to the classicaldigital processor.
 15. The method of claim 1, further comprising:examining at least a portion of the query image prior to comparing thegraph representation of the query image with the graph representationsof the database images; and identifying an aspect of the query imagethat is common to a subset of the database images, and wherein comparinga graph representation of the at least one feature of a query image to arespective graph representation of each of at least some of a pluralityof database images includes comparing the graph representation of the atleast one feature of the query image to only the graph representation ofthe databases images in the subset of the database images, withcorresponding association graphs being produced therefor.
 16. The methodof claim 1 wherein the at least one feature of the query imagerepresents a majority of the query image.
 17. The method of claim 1wherein the similarity between the feature of the query image and the atleast a portion of the respective database image to which theassociation graph corresponds is indicative of whether or not the atleast one feature of the query image occurs within the respectivedatabase image to which the association graph corresponds.
 18. Acomputer-implemented method of solving image matching problems, themethod comprising: casting an image matching problem as a quadraticunconstrained binary optimization problem; mapping the quadraticunconstrained binary optimization problem to a quantum processor; andevolving the quantum processor to produce a solution to the quadraticunconstrained binary optimization problem.
 19. A computer-implementedmethod of comparing two objects, the method comprising: comparing agraph representation of at least a portion of a first object to a graphrepresentation of at least a portion of a second object, wherein thecomparison includes generating an association graph; and determining atleast one characteristic of the association graph via a quantumprocessor, wherein the at least one characteristic of the associationgraph is representative of a similarity between the at least a portionof the first object and the at least a portion of the second object. 20.The method of claim 19 wherein the first object and the second objectare both images.
 21. The method of claim 19 wherein determining at leastone characteristic of the association graph includes determining amaximum independent set of the association graph.
 22. The method ofclaim 19 wherein determining at least one characteristic of theassociation graph includes determining a maximum clique of theassociation graph.
 23. The method of claim 19 determining at least onecharacteristic of the association graph results in the quantum processorreturning a value that is representative of a measure of similaritybetween the at least a portion of the first object and the at least aportion of the second object.